Post on 10-Mar-2020
EOC Review.notebook May 14, 2013
Rational and Irrational Numbers
Rational Numbers
Ex. .6767... Ex. .5 .03 a decimal that terminates
a decimal that repeats indefinitely positive and negative whole numbers
Integers ..., 3, 2, 1, 0, 1, 2, 3,...
Whole numbers and their negatives.Not DecimalsNot Fractions
INTEGERS = RATIONAL NUMBERS
5, -8, 9, -25, 0, -12, 2
.6, -.08, 2/5, -1.2, 1/9
EOC Review.notebook May 14, 2013
Nonterminating (never stops) Nonrepeating decimals (never repeats)
Irrational Numbers
Examples of irrational numbers
EOC Review.notebook May 14, 2013
EOC Review.notebook May 14, 2013
Unit 1 – Equaons
• Equaons
To solve an equaon, use your calculator.
STEPS:
1. Menu
2. Algebra (#3)
3. Numerical Solve (#1)
4. Type in equaon
5. Put a comma (,) at the end, and then the variable aerwards
EOC Review.notebook May 14, 2013
Ex 1: 2x + 5 = 6x – 3
Ex 2: 6(x + 1) = 2/3(9x + 12)
Ex 3: 4x + 10 = 2(2x + 5)
Ex 4:
EOC Review.notebook May 14, 2013
Solve: cd = f + gh for h
EOC Review.notebook May 14, 2013
Dimensional Analysis
• Must Know Conversions!!!!
Dimensional Analysis:
Ex 1: The sea horse swims at a rate of 52.68 feet per hour. Use dimensional analysis to convert this speed to inches per minute.
EOC Review.notebook May 14, 2013
Ex 2: A car is traveling at 50 miles per hour. How many feet per second is the car traveling?
• Inequalies:
o Solve the same as equaons
o If there is a negave with the variable, flip the sign
o Variable must always be on the le, the answer must be on the right
o > and < are open circles on the number line
o ≤ and ≥ are closed circles on the number line
o > and ≥ are to the right on the number line
o < and ≤ are to the le on the number line
EOC Review.notebook May 14, 2013
Ex 1: y ≤ 4y + 18
Ex 2: 4m – 3 < 2m + 6
EOC Review.notebook May 14, 2013
Ex 3: 2(k – 3) > 6 + 3k – 3
EOC Review.notebook May 14, 2013
EOC Review.notebook May 14, 2013
Relation: Any set of ordered pairsRelations can be represented as the following:
set of ordered pairs tablegraph mapping
(1,2)(2,4)(0,3)
x y 12 0
2 43
12 0
2 43
Function:
• A relation where there is only one x for every y
• the x's cannot repeat!
EOC Review.notebook May 14, 2013
"x" and "y" coordinates in each ordered pair are switched .**The Domain becomes the Range in the inverse.**
RELATION INVERSE RELATION
Inverse Relation
(2,5)(3,2)(6,7)(5,1)
(5,2)(2,3)(7,6)(1,5)
Example 1:Express the relation (3,2), (-1,4), (0,-3), (-3,4), and (-2,-2)as a table, graph, and a mapping. Tell the domain and range.
x yx y
A. What is the domain of the relaon?
B. What is the range of the relaon?
C. Is the relaon a funcon? Explain your answer.
D. What is the inverse of the relaon as ordered pairs?
E. Is the inverse of the relaon a funcon? Explain your answer.
EOC Review.notebook May 14, 2013
EOC Review.notebook May 14, 2013
linear function:
• a function whose graph is linear and a non vertical line
• a table or scenario that has a constant rate of change
• any equation set equal to y that does not have any variables
• raised to a power, does not have any variables in a
• denominator and does not have any variables being multiplied
EOC Review.notebook May 14, 2013
The xintercept is where the graph crosses the xaxis.
The ycoordinate is always 0.
The yintercept is where the graph crosses the yaxis.
The xcoordinate is always 0.
Try These:
Find the x and y intercepts of the following equations.
ex1. 9x 6y = 18
ex2. 5x + 4y = 15
ex3. 21x + 42y = 63
EOC Review.notebook May 14, 2013
Definitions of Slope:
1. Constant Rate of Change
2. RISE
3. The increase or decrease of a graph, table, ordered pairs or a situation
4.The change in y's
RUN
The change in x's
EOC Review.notebook May 14, 2013
EOC Review.notebook May 14, 2013
Slope – Intercept Form
y = mx + b
m represents the slope (rate of change)
b represents the yintercept
yintercept: Where the graph crosses the
yaxis
EOC Review.notebook May 14, 2013
Ex 1: What is the equaon 4x + 6y = ‐12 in slope intercept from?
Ex 2: What is the equaon of the line that passes through the point with
coordinates (‐5, 3) and has a slope of
EOC Review.notebook May 14, 2013
Ex 3: What is the equaon of this line?
Ex 4: Use funcon notaon to represent the funcon shown in this graph:
EOC Review.notebook May 14, 2013
Ex 5: Which equaon has this graph?
Ex 6: Which is the graph of
EOC Review.notebook May 14, 2013
Ex 7: Which is the graph of the line that passes through the point with the coordinates of (1, 3) and has a slope of ½?
Point‐Slope Form:
1. What is the equaon for point‐ slope form?__________________________________
2. What two things do you need to write an equaon in point‐slope form?__________________________________
EOC Review.notebook May 14, 2013
3. Where do you plug in the slope?__________________________________
4. Where do you plug in the point?___________________________________
EOC Review.notebook May 14, 2013
Parallel Lines: The equations have the same slope; the graphs never intersect
Perpendicular Lines: The equations have slope that are opposite reciprocals; The graphs cross to form a right angle
Example 1: Write an equaon of a line in slope‐intercept form that is parallel to y = ‐3x ‐ 2 and goes through (‐1, ‐2)
Example 2: Write the equaon of a line in slope‐intercept form that is perpendicular to x + 4y = 12 and passes through (0, ‐3)
EOC Review.notebook May 14, 2013
Example 3: Which of the lines whose equaons are given below is perpendicular to y = 4x + 3?
Scaer Plots:
Steps:
1. Enter your data into the lists and spreadsheets on the home screen of the calculator (looks like excel sheet)
2. Go back to the home screen and open data and stascs (looks like a bar graph)
3. Add your x and y variables
4. Press menu; pick analyze (#4) recession (#6) and y = mx + b (#1)
EOC Review.notebook May 14, 2013
Translaons:
What affect does slope have on a graph?
m > 1_____________________________________________
0<m<1____________________________________________
m < 0_____________________________________________
EOC Review.notebook May 14, 2013
EOC Review.notebook May 14, 2013
EOC Review.notebook May 14, 2013
EOC Review.notebook May 14, 2013
Steps:
1. Get rid of outside exponent
2. Move negative exponents
3. Combine like bases and whole numbers
mult by allinside exponents
neg on top→ move to bottomneg on bottom → movet to top
• If variables are on same level, (x 4x5), add exponents• If variables Are on different levels, subtract exponents• If numbers are on same level, multiply them• if numbers are on different levels, divide them
EOC Review.notebook May 14, 2013
EOC Review.notebook May 14, 2013
EOC Review.notebook May 14, 2013
EOC Review.notebook May 14, 2013
EOC Review.notebook May 14, 2013
EOC Review.notebook May 14, 2013
Equation: y = kx
SetUp: y = yx x
Graph:
goes thruthe point(0, 0)
Variables:
When the x's increase, the y's increase
When the x's decrease, the y's decrease
K is the Slope, Rate of change, or the constant of variation
EOC Review.notebook May 14, 2013
Equation: y = kx
SetUp: y = yx x
Graph:
goes thruthe point(0, 0)
Variables:
When the x's increase, the y's increase
When the x's decrease, the y's decrease
K is the Slope, Rate of change, or the constant of variation
EOC Review.notebook May 14, 2013